ADMISSIBLE (REES) EXACT SEQUENCES AND FLAT ACTS

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran.

Abstract

Let $S$ be a commutative pointed monoid.
In this paper, some properties of admissible (Rees)
short exact sequences of $S$-acts are investigated.
In particular, it is shown that every admissible short exact sequence
of $S$-acts is Rees short exact.
In addition, a characterization of flat acts via preserving
admissible short exact sequences is established.
As a consequence, we show that for a flat $S$-act $F$, the functor
$F \otimes_{S} -$ preserves admissible morphisms.
Finally, it is proved that the class of flat $S$-acts is a subclass of
admissibly projective ones.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 327-346

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